Theorems · Theorem · nonassociative algebras

LieModule.toEnd_lie

∀ (R : Type u) {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M] (x y : L)
  (z : M), ((LieModule.toEnd R L M) x) ⁅y, z⁆ = ⁅((LieAlgebra.ad R L) x) y, z⁆ + ⁅y, ((LieModule.toEnd R L M) x) z⁆

Defined in

Mathlib.Algebra.Lie.OfAssociative

Cited by

2 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule